If the carrying value $($remaining loan balance$)$ of a $$20,000$ installment note of with an interest rate of $10\%$ was reduced by $$1,000$ at the end of the first year, what would be the interest expense in the second year?

a$)$ $$100$

c$)$ $$1,900$

b$)$ $$1,000$

d$)$ $$2,000$